Math, asked by rpxexclusive8210, 9 months ago

Find the sum of 3 upon root 5 + root 5 + 7 root 5 +...to 15 term

Answers

Answered by mihir2695

Answer:

here is your answer

Step-by-step explanation:

Question mistake

it will be 7/√5

now after omitting mistake it will be come an A.P

now common difference is

√5-3/√5=7/√5-√5=2/√5

now sum of terms in A.P is

S=n/2(2a+(n-1)d)

Putting value of n=15 a=3/√5 and d=2/√5 in above situation we get

S=15/2(2√3/5+(15-1)√2/5)

i hope it will be helpful

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{51 \sqrt{5} }$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

The given AP :

$\Large{ \frac{3}{ \sqrt{5} } + \sqrt{5} + \frac{7}{ \sqrt{5} } ...............}$

first term, a $\large{ = \frac{3}{ \sqrt{5} } }$

common difference, d $\large{ = \left( \frac{3}{ \sqrt{5} } - \sqrt{5} \right) = \left( \sqrt{5} - \frac{7}{ \sqrt{5} } \right) = \left( \frac{2}{ \sqrt{5} } \right) }$

number of terms, n = 15

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

Sum of n ( 15 ) terms

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Arithmetic Progression ( A.P. )

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We have,

$\Large{S_n = \frac{n}{2} [ 2a + ( n - 1 )d ]}$

$\therefore \: \:$ ,

$\Large{ \longmapsto S_1_5 = \frac{15}{2} [ 2a + ( 15 - 1 )d ]}$

$\Large{ \implies S_1_5 = \frac{15}{2} [ 2a + 14d ]}$

$\Large{ \implies S_1_5 = \frac{15}{2} \times 2[ a + 7d ]}$

$\Large{ \implies S_1_5 = \frac{15}{ \cancel{2} } \times \cancel{2} [ a + 7d ]}$

$\Large{ \implies S_1_5 = 15 \times [ a + 7d ]}$

$\Large{ \implies S_1_5 = 15 \times \left[ \frac{3}{ \sqrt{5} } + 7 \left( \frac{2}{ \sqrt{5} } \right) \right] }$

$\Large{ \implies S_1_5 = 15 \times \left[ \frac{3}{ \sqrt{5} } + \frac{14}{ \sqrt{5} } \right] }$

$\Large{ \implies S_1_5 = 15 \times \left[ \frac{3 + 14}{ \sqrt{5} } \right] }$

$\Large{ \implies S_1_5 = 15 \times \left[ \frac{17}{ \sqrt{5} } \right] }$

$\Large{ \implies S_1_5 = \sqrt{5} \times \sqrt{5} \times 3 \times \left[ \frac{17}{ \sqrt{5} } \right] }$

$\Large{ \implies S_1_5 = \sqrt{5} \times 1 \times 3 \times \left[ \frac{17}{1} \right] }$

$\Large{ \implies S_1_5 = \sqrt{5} \times 3 \times 17}$

$\Large{ \implies S_1_5 = \sqrt{5} \times 51}$

$\Large{ \implies S_1_5 = 51 \sqrt{5} }$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

Hence, sum of all terms $\large{ = 51 \sqrt{5} }$

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